The best of ideas is hurt by uncritical acceptance and thrives on critical examination.
Interpretation
Ideas flourish under scrutiny and suffer from blind acceptance.
George Polya emphasizes the importance of critical thinking in the evaluation of ideas. Accepting ideas without question can lead to stagnation, while subjecting them to rigorous examination can enhance understanding and innovation.
In practice
During a team meeting, I reminded everyone that the best solutions come from questioning our assumptions.
Pedantry and mastery are opposite attitudes toward rules. To apply a rule to the letter, rigidly, unquestioningly, in cases where it fits and in cases where it does not fit, is pedantry. [...] To apply a rule with natural ease, with judgment, noticing the cases where it fits, and without ever letting the words of the rule obscure the purpose of the action or the opportunities of the situation, is mastery.
If you wish to learn swimming you have to go into the water and if you wish to become a problem solver you have to solve problems.
To teach effectively a teacher must develop a feeling for his subject; he cannot make his students sense its vitality if he does not sense it himself. He cannot share his enthusiasm when he has no enthusiasm to share. How he makes his point may be as important as the point he makes; he must personally feel it to be important.
Mathematics is not a spectator sport!
Mathematics is being lazy. Mathematics is letting the principles do the work for you so that you do not have to do the work for yourself
In order to translate a sentence from English into French two things are necessary. First, we must understand thoroughly the English sentence. Second, we must be familiar with the forms of expression peculiar to the French language. The situation is very similar when we attempt to express in mathematical symbols a condition proposed in words. First, we must understand thoroughly the condition. Second, we must be familiar with the forms of mathematical expression.
There is no pleasure without a tincture of bitterness.
The surgeons' market is imaginary, since there is nothing wrong with women's faces or bodies that social change won't cure; so the surgeons depend for their income on warping female self-perception and multiplying female self-hatred.
Why was I chosen?' 'Such questions cannot be answered,' said Gandalf. 'You may be sure that it was not for any merit that others do not possess. But you have been chosen, and you must therefore use such strength and heart and wits as you have.
When intelligent people pride themselves on not understanding, it is quite natural they should succeed better than fools.
I found I wasn't asking good enough questions because I assumed I knew something.
Unless a man feels he has a good enough memory, he should never venture to lie.
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